Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.

Characterisation, cloning and production of industrially interesting enzymes: gluconolactone oxidase of Penicillium cyaneo-fulvum and gluconate 5-dehydrogenase of Gluconobacter suboxydans

The work covered in this thesis is focused on the development of technology for bioconversion of glucose into D-erythorbic acid (D-EA) and 5-ketogluconic acid (5-KGA). The task was to show on proof-of-concept level the functionality of the enzymatic conversion or one-step bioconversion of glucose to these acids. The feasibility of both studies to be further developed for production processes was also evaluated. The glucose - D-EA bioconversion study was based on the use of a cloned gene encoding a D-EA forming soluble flavoprotein, D-gluconolactone oxidase (GLO). GLO was purified from Penicillium cyaneo-fulvum and partially sequenced. The peptide sequences obtained were used to isolate a cDNA clone encoding the enzyme. The cloned gene (GenBank accession no. AY576053) is homologous to the other known eukaryotic lactone oxidases and also to some putative prokaryotic lactone oxidases. Analysis of the deduced protein sequence of GLO indicated the presence of a typical secretion signal sequence at the N-terminus of the enzyme. No other targeting/anchoring signals were found, suggesting that GLO is the first known lactone oxidase that is secreted rather than targeted to the membranes of the endoplasmic reticulum or mitochondria. Experimental evidence supports this analysis, as near complete secretion of GLO was observed in two different yeast expression systems. Highest expression levels of GLO were obtained using Pichia pastoris as an expression host. Recombinant GLO was characterised and the suitability of purified GLO for the production of D-EA was studied. Immobilised GLO was found to be rapidly inactivated during D-EA production. The feasibility of in vivo glucose - D-EA conversion using a P. pastoris strain co-expressing the genes of GLO and glucose oxidase (GOD, E.C. 1.1.3.4) of A. niger was demonstrated. The glucose - 5-KGA bioconversion study followed a similar strategy to that used in the D-EA production research. The rationale was based on the use of a cloned gene encoding a membrane-bound pyrroloquinoline quinone (PQQ)-dependent gluconate 5-dehydrogenase (GA 5-DH). GA 5-DH was purified to homogeneity from the only source of this enzyme known in literature, Gluconobacter suboxydans, and partially sequenced. Using the amino acid sequence information, the GA 5-DH gene was cloned from a genomic library of G. suboxydans. The cloned gene was sequenced (GenBank accession no. AJ577472) and found to be an operon of two adjacent genes encoding two subunits of GA 5-DH. It turned out that GA 5-DH is a rather close homologue of a sorbitol dehydrogenase from another G. suboxydans strain. It was also found that GA 5-DH has significant polyol dehydrogenase activity. The G. suboxydans GA 5-DH gene was poorly expressed in E. coli. Under optimised conditions maximum expression levels of GA 5-DH did not exceed the levels found in wild-type G. suboxydans. Attempts to increase expression levels resulted in repression of growth and extensive cell lysis. However, the expression levels were sufficient to demonstrate the possibility of bioconversion of glucose and gluconate into 5-KGA using recombinant strains of E. coli. An uncharacterised homologue of GA 5-DH was identified in Xanthomonas campestris using in silico screening. This enzyme encoded by chromosomal locus NP_636946 was found by a sequencing project of X. campestris and named as a hypothetical glucose dehydrogenase. The gene encoding this uncharacterised enzyme was cloned, expressed in E. coli and found to encode a gluconate/polyol dehydrogenase without glucose dehydrogenase activity. Moreover, the X. campestris GA 5-DH gene was expressed in E. coli at nearly 30 times higher levels than the G. suboxydans GA 5-DH gene. Good expressability of the X. campestris GA-5DH gene makes it a valuable tool not only for 5-KGA production in the tartaric acid (TA) bioprocess, but possibly also for other bioprocesses (e.g. oxidation of sorbitol into L-sorbose). In addition to glucose - 5-KGA bioconversion, a preliminary study of the feasibility of enzymatic conversion of 5-KGA into TA was carried out. Here, the efficacy of the first step of a prospective two-step conversion route including a transketolase and a dehydrogenase was confirmed. It was found that transketolase convert 5-KGA into TA semialdehyde. A candidate for the second step was suggested to be succinic dehydrogenase, but this was not tested. The analysis of the two subprojects indicated that bioconversion of glucose to TA using X. campestris GA 5-DH should be prioritised first and the process development efforts in future should be focused on development of more efficient GA 5-DH production strains by screening a more suitable production host and by protein engineering.